# using Relativity and Time Dilation to travel to the future **URL:** \ **Category:** Factual Questions\ **Created:** [June 28, 2010, 9:05am UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765 "2010-06-28T09:05:07Z")\ **Posts on this page:** 18\ **Page:** 1
**Author:** ![AllFreedomUnlessDefyingScience](https://avatars.discourse-cdn.com/v4/letter/a/e36b37/32.png) [@AllFreedomUnlessDefyingScience](https://boards.straightdope.com/u/AllFreedomUnlessDefyingScience)\ **Post date:** [June 28, 2010, 9:05am UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/1 "2010-06-28T09:05:07Z")
I’d like to know how fast you would have to be going to take a LONG jump forward into the future using the Time Dilation caused at speeds approaching that of light, however the math involved is beyond me. I’m specifically curious about how fast you need to be going in order to turn a 50 year journey into a 10 billion, 30 billion, 50 billion and 100 billion year leap. Can anyone help me with the answer? Thanks for all replies, AllFree ---
**Author:** ![BMalion](https://avatars.discourse-cdn.com/v4/letter/b/e274bd/32.png) [@BMalion](https://boards.straightdope.com/u/BMalion)\ **Post date:** [June 28, 2010, 11:01am UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/2 "2010-06-28T11:01:42Z")
Thinking of taking a trip? ---
**Author:** ![AllFreedomUnlessDefyingScience](https://avatars.discourse-cdn.com/v4/letter/a/e36b37/32.png) [@AllFreedomUnlessDefyingScience](https://boards.straightdope.com/u/AllFreedomUnlessDefyingScience)\ **Post date:** [June 28, 2010, 11:45am UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/3 "2010-06-28T11:45:30Z")
> [@BMalion](#): > > Thinking of taking a trip? I don’t foresee the technology for this existing in my lifetime, but seeing the end of the universe would make for a hell of a sightseeing trip. ---
**Author:** ![Rhythmdvl](https://avatars.discourse-cdn.com/v4/letter/r/85f322/32.png) [@Rhythmdvl](https://boards.straightdope.com/u/Rhythmdvl)\ **Post date:** [June 28, 2010, 12:28pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/4 "2010-06-28T12:28:49Z")
> [@AllFreedomUnlessDefyingScience](#): > > I don’t foresee the technology for this existing in my lifetime, but seeing the end of the universe would make for a hell of a sightseeing trip. Be sure to make reservations at Milliways. ---
**Author:** ![Keeve](https://avatars.discourse-cdn.com/v4/letter/k/f07891/32.png) [@Keeve](https://boards.straightdope.com/u/Keeve)\ **Post date:** [June 28, 2010, 12:51pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/5 "2010-06-28T12:51:41Z")
The formula for answering the OP is available in Wikipedia [here](http://en.wikipedia.org/wiki/Time_dilation#Overview_of_time_dilation_formulae). Sorry, but I don’t have time right now to work out the answers. Maybe someone else? ---
**Author:** ![Keeve](https://avatars.discourse-cdn.com/v4/letter/k/f07891/32.png) [@Keeve](https://boards.straightdope.com/u/Keeve)\ **Post date:** [June 28, 2010, 12:58pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/6 "2010-06-28T12:58:11Z")
Wow. Google is your friend. I entered “time dilation calculator”, and got a whole bunch of sites, one of which showed that going 99.999999999% of the speed of light would stretch 50 years to be 11,180,308 years. I could’ve added more nines, but the input box made it hard to read. ---
**Author:** ![AllFreedomUnlessDefyingScience](https://avatars.discourse-cdn.com/v4/letter/a/e36b37/32.png) [@AllFreedomUnlessDefyingScience](https://boards.straightdope.com/u/AllFreedomUnlessDefyingScience)\ **Post date:** [June 28, 2010, 1:05pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/7 "2010-06-28T13:05:39Z")
> [@Keeve](#): > > Wow. Google is your friend. I entered “time dilation calculator”, and got a whole bunch of sites, one of which showed that going 99.999999999% of the speed of light would stretch 50 years to be 11,180,308 years. I couldve added more nines, but the input box made it hard to read. None of the sights I found could perform the calculation from the standpoint of ratio of time, only tell you how much time it will take if you enter the velocity. Can anyone recommend a web site that can handle the calculations the other way around? ---
**Author:** ![Superfluous\_Parentheses](https://avatars.discourse-cdn.com/v4/letter/s/8edcca/32.png) [@Superfluous\_Parentheses](https://boards.straightdope.com/u/Superfluous_Parentheses)\ **Post date:** [June 28, 2010, 2:03pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/8 "2010-06-28T14:03:41Z")
> [@AllFreedomUnlessDefyingScience](#): > > None of the sights I found could perform the calculation from the standpoint of ratio of time, only tell you how much time it will take if you enter the velocity. Can anyone recommend a web site that can handle the calculations the other way around? The actual formula is fairly simple to derive if you set c to 1 in the formula from Wiki **Keeve** pointed to: v = sqrt(1 - ratio) where ratio is moving time / proper time, so 50 / 10000000000 for your first example. 50/10 billion -\> 0.9999999975 c 50/30 billion -\> 0.9999999991666666 c 50/100 billion -\> 0.99999999975 c ---
**Author:** ![AllFreedomUnlessDefyingScience](https://avatars.discourse-cdn.com/v4/letter/a/e36b37/32.png) [@AllFreedomUnlessDefyingScience](https://boards.straightdope.com/u/AllFreedomUnlessDefyingScience)\ **Post date:** [June 28, 2010, 2:26pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/9 "2010-06-28T14:26:56Z")
> [@Superfluous\_Parentheses](#): > > The actual formula is fairly simple to derive if you set c to 1 in the formula from Wiki **Keeve** pointed to: > > v = sqrt(1 - ratio) > > where ratio is moving time / proper time, so 50 / 10000000000 for your first example. > > 50/10 billion -\> 0.9999999975 c > 50/30 billion -\> 0.9999999991666666 c > 50/100 billion -\> 0.99999999975 c Thank you very much, that tells me what I wanted to know. If anyone else has anything to add however feel free. ---
**Author:** ![Grey](https://avatars.discourse-cdn.com/v4/letter/g/b782af/32.png) [@Grey](https://boards.straightdope.com/u/Grey)\ **Post date:** [June 28, 2010, 2:30pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/10 "2010-06-28T14:30:41Z")
Sure - end of the universe should be around the evaporation of a galaxy mass black holes - 10[sup]100[/sup] years. Better go faster. ---
**Author:** ![AllFreedomUnlessDefyingScience](https://avatars.discourse-cdn.com/v4/letter/a/e36b37/32.png) [@AllFreedomUnlessDefyingScience](https://boards.straightdope.com/u/AllFreedomUnlessDefyingScience)\ **Post date:** [June 28, 2010, 2:46pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/11 "2010-06-28T14:46:20Z")
> [@Grey](#): > > Sure - end of the universe should be around the evaporation of a galaxy mass black holes - 10[sup]100[/sup] years. > > Better go faster. Well, I don’t suppose that figure will fit into most online conversion programs. Does anyone care to put forward the speed that sort of time dilation would require? ---
**Author:** ![Superfluous\_Parentheses](https://avatars.discourse-cdn.com/v4/letter/s/8edcca/32.png) [@Superfluous\_Parentheses](https://boards.straightdope.com/u/Superfluous_Parentheses)\ **Post date:** [June 28, 2010, 3:16pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/12 "2010-06-28T15:16:13Z")
If I haven’t messed up in my arbitrary precision calculator, it’s roughly 0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999975 c ---
**Author:** ![beowulff](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/beowulff/32/542_2.png) [@beowulff](https://boards.straightdope.com/u/beowulff)\ **Post date:** [June 28, 2010, 3:19pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/13 "2010-06-28T15:19:36Z")
> [@Rhythmdvl](#): > > Be sure to make reservations at Milliways. Would you please give my regards to Zarquon? ---
**Author:** ![Smeghead](https://avatars.discourse-cdn.com/v4/letter/s/f1d935/32.png) [@Smeghead](https://boards.straightdope.com/u/Smeghead)\ **Post date:** [June 28, 2010, 3:33pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/14 "2010-06-28T15:33:43Z")
What the…? This is the Big Bang Burger Barn! I knew we should have taken that left at Alberquerque. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [June 28, 2010, 4:06pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/15 "2010-06-28T16:06:26Z")
> [@Superfluous\_Parentheses](#): > > v = sqrt(1 - ratio) Surely, you mean v = sqrt(1 - ratio^2). ---
**Author:** ![Superfluous\_Parentheses](https://avatars.discourse-cdn.com/v4/letter/s/8edcca/32.png) [@Superfluous\_Parentheses](https://boards.straightdope.com/u/Superfluous_Parentheses)\ **Post date:** [June 28, 2010, 4:34pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/16 "2010-06-28T16:34:21Z")
> [@Indistinguishable](#): > > Surely, you mean v = sqrt(1 - ratio^2). Erm… Yes that what I should have meant. But somewhere, that power of two got lost. So my calculations are all significantly off. ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [June 28, 2010, 11:16pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/17 "2010-06-28T23:16:23Z")
> [@Indistinguishable](#): > > Surely, you mean v = sqrt(1 - ratio^2). For small values of ratio, by the way, this is very close to v = 1 - (ratio)[sup]2[/sup]/2. If you run out of 9’s on your calculator, use this approximation instead. ---
**Author:** ![Chipacabra](https://avatars.discourse-cdn.com/v4/letter/c/e19b73/32.png) [@Chipacabra](https://boards.straightdope.com/u/Chipacabra)\ **Post date:** [June 28, 2010, 11:53pm UTC](https://boards.straightdope.com/t/using-relativity-and-time-dilation-to-travel-to-the-future/544765/18 "2010-06-28T23:53:32Z")
Also, most time dilation calculations assume you’re traveling at a constant velocity. That’s fine if you have some sort of magic warp drive, but if we DO start traveling to other systems, we probably want constant thrust (acceleration) drives. In that case, you need an equation where you can plug in your acceleration (often in units of gravities) and the total distance. I used to have that equation handy, but don’t anymore. I should really dig it up.